Gaming terminals, such as slot machines, video poker machines and the like, have been a cornerstone of the gaming industry for many years. Generally, the popularity of such machines with players is dependent on the likelihood (or perceived likelihood) of winning money at the gaming terminal and the intrinsic entertainment value of the machine relative to other available gaming options. Where the available gaming options include a number of competing machines and the expectation of winning on each machine is roughly the same (or believed to be the same), players are most likely to be attracted to the most entertaining and exciting machines. Shrewd operators constantly strive to employ the most entertaining and exciting machines available because such machines attract frequent play and, hence, increase profitability to the operator.
One method of attracting players to gaming terminals is by providing a bonus game in addition to a basic game. Generally, bonus games provide a greater expectation of winning than the basic game alone. According to one type of bonus game, a plurality of player-selectable symbols or windows are provided and the selection of which reveals a bonus-credit award that is initially covered by the symbol. The player continues to make selections and accumulate awards until an end-bonus outcome is uncovered. Thus, if a player initially selects a symbol covering the end-bonus outcome, the player receives no bonus award. This selection-type game, wherein a selection may award credits or end the game, is generally considered to have a high volatility index. “Volatility index” is a mathematical value that is the industry standard for measuring distribution of sizes and probabilities of slot machine payoffs and is described in further detail in U.S. Pat. No. 6,302,791, which is incorporated herein by reference in its entirety. For example, standard slot machines have a relatively steady payoff progression and, thus, are considered to have low volatility indices, which means that there is a relatively steady progression of many payoff values from the lowest to the highest, with each payoff corresponding probability decreasing as the value of the payoff increases. On the other hand, the described selection-type bonus game has a high volatility index. The present invention is directed to moderating the level of volatility in a selection-type game.